2.1.1 PMMC The Permanent Magnet Moving Coil (PMMC) galvanometer used for dc measurement only. The motor action is produced by the flow of a small current throught a moving coil which is positioned in the field of a permanent magnet The basic moving coil system-D’Arsonval galvonometer
2.1.3 Deflecting Torque Resulting from the effects of magnetic electrostatic. This torque causes the pointer moves from the zero position F IRON CORE N S F
DEFLECTING TORQUE Td = BANI (Nm)B = flux density in Wb/m2 or Tesla (T)N = number of coilsA = Area cross-section (length (l) x coil diameter (d)m2 )I = current flowing through the coil - Ampere
2.1.4 DAMPING CURVE Works to speed up the pointer stops Pointer may oscillate before the show reading and damping torque required to accelerate the needle stops.
Damping curve V Under damp Critical damp Steady state Over damp t 0
2.1.5 Damping Curve Over damp – pointer will move slowly and never reach the steady state. The value will be less than the actual value. Under damp - pointer will oscillate until it finally reach the final value. The result is difficult to read. Critical damp - pointer to achieve the true value of free oscillations in a short time.
2.1.6 Types of dampingEddy current dampingAir friction dampingFluid damping
EDDY CURRENT DAMPING An aluminum disc D, is controlled by a reel, can be move between a the pole of a permanent magnet M. If the disk moves clockwise, the e.m.f induced in the disc circulate eddy currents distribution as shown (interrupted lines). From Lenz Law, the current will impose a force against the movement of their forms. Therefore, the resulting damping force is counter clockwise. M D
Air friction DampingA piece of the blade is attached to the moving parts in the meter. Resistance produced by the air around will give the desired damping.
Fluid damping The same principle is used but the blade is allowed to move in a container of liquid with suitable viscosity.
2.2 DC VOLTMETER The basic d’Arsonval meter can be converted to a dc voltmeter by connecting a multiplier Rs in series with it as shown in Figure 2.6. The purpose of the multiplier is to extend the range of the meter and to limit the current through the d’Arsonval meter to the maximum full-scale deflection current.
2.2.1 Basic DC Voltmeter circuit Figure 2.6To find the value of the multiplier resistor, we may first determinethe sensitivity, S, of the d’Arsonval. If the sensitivity is known, thetotal voltmeter resistance can be calculated easily.The sensitivity of a voltmeter is always specified by themanufacturer, and is frequently printed on the scale of theinstrument.
Voltmeter• If the full-scale meter current is known, the sensitivity can be determined as the reciprocal of the full scale current. Sensitivity = 1 / Ifs Where Ifs is the full-scale deflection current of d’Arsonval meter.
2.2.2 Multiplier Resistance Thevalue of the multiplier resistance can be found using this relationship: Rs + Rm = S x Vrange Thus, Rs = (S x Vrange) - Rm
2.2.3 Example Calculate the value of the multiplier resistance on the 50 V range of a dc voltmeter that used a 500μA d’Arsonval meter with an internal resistance of 1 kΩ.
Solution : S = 1/Ifs = 1/500µA = 2KΩ/V Rs = S x Range – Rm = 2 kΩ/V x 50 V – 1 kΩ = 99 kΩ
2.2.4 Multi range Voltmeter A multi range voltmeter consists of a deflection instrument, several multiplier resistors and a rotary switch. Two possible circuits are illustrated in Figure 2.7 (a) and (b). Figure 2.7(a): Multirange Voltmeter
Infigure 2.7 (a) only one of the three multiplier resistors is connected in series with the meter at any time. The range of this meter is V = Im ( R + Rm ) Where the multiplier resistance, R can be R1 or R2 or R3.
Figure 2.7(b): A commercial version of a multi range voltmeter
In figure 2.7(b) the multiplier resistors are connected in series, and each junction is connected to one of the switch terminals. The range of this voltmeter can be also calculated from the equation V = Im (Rm + R) Where the multiplier, R, now can be R3 or (R3 + R2) or (R1 + R2 + R3) (Note: the largest voltage range must be associated with the largest sum of the multiplier resistance)
2.2.5 Example Calculate the value of the multiplier resistance for the multiple range dc voltmeter circuit shown in Figure 2.7(a) and Figure 2.7(b), if Ifs = 50μA and Rm = 1kΩ
2.2.7DC Voltmeter Loading Effect Asthe DC ammeter, the DC voltmeter also observe for loading effect whenever it is inserted to a measured circuit. Figure 2.7 shows a circuit with the DC voltmeter is inserted into it. Inserting voltmeter always increase the resistance and decrease the current flowing through the circuit.
Figure 2.7: Circuit with voltmeter insertion effect
Withoutthe insertion of the DC voltmeter, the voltage VRB can be found as: RB VRB = _______ X E RB + RA
2.2.8 LOADING EFFECT Inserting the voltmeter in parallel with RB gives us the total inserted resistance as : RT = RS + RM Thus, yield to Req = RB //RT
m Now, the voltage VRB with the voltmeter insertion is found as: Req VRB = ________ x E Req + RA
Therefore, m Insertion error = VRB – VRB X 100% VRB
DC VoltmeterExample 1. Calculate the value of the multiplier Rs on the 50-V range of a DC Voltmeter that used 200-µA meter movements with an internal resistance of 1.2kΩ.
DC VoltmeterExample 2. Calculate the values of Rs for the multiple- range DC Voltmeter circuits as shown below:
DC VoltmeterExample 3. Calculate the values of Rs for the multiple- range DC Voltmeter circuits as shown below:
Voltmeter Loading Effects When a voltmeter is used to measure the voltage across a circuit component, the voltmeter circuit itself is in parallel with the circuit component. Since the parallel combination of two resistors is less than either resistor alone, the resistor seen by the source is less with the voltmeter connector than without.
Voltmeter Loading Effects Therefore, the voltage across the component is less whenever the voltmeter is connected. The decrease in voltage maybe negligible or appreciable, depending on the Sensitivity of the voltmeter being used. This effect is called voltmeter loading and the resulting error is called loading error.
Voltmeter Loading EffectsExample 5: Two different voltmeters are used to measure the voltage across RB in the circuit below. The meters are: Meter A : S= 1kΩ/V;Rm=0.2kΩ; Range =10V Meter B : S=20kΩ/V;Rm=2.2kΩ; Range = 10V Calculate: Voltage across RB without any meter. Voltage across RB when meter A is used. Voltage across RB when meter B is used. Loading Errors in both voltmeter readings.
Voltmeter Loading EffectsExample 6: Find the voltage reading and the percentage of loading error of each reading obtained with a voltmeter on: Its 5-V range. Its 10-V range Its 50-V range. The meter has a 20-kΩ/V sensitivity and connected across RA.